1. Field of the Invention
The present invention relates to a method of and apparatus for extracting model parameters for use in the process, device or circuit simulation of a semiconductor integrated circuit.
2. Description of the Related Art
Process simulation means making a model of a physical or chemical change in the material of, for example, a substrate in the semiconductor device manufacturing steps, such as ion implantation, oxidation, diffusion, epitaxial growth, etching, deposition and lithography and obtaining an impurity distribution or a device shape after these steps by using a calculator. Device simulation means obtaining device characteristics from the behavior of carriers within a device based on the physical shape of the device and the impurity distribution thereof. Circuit simulation means studying operation characteristics on a basic gate or a functional cell using a circuit simulator while considering the manufacturing variations, temperature and aged deterioration of a device. One reason such simulation is utilized and required more frequently than before is that it takes greater time from the determination of a specification to design to manufacture as larger-scale integrated circuits are increasingly manufactured. The simulation method as described above has met the above-mentioned demand and been developed to obtain more precise analysis results.
It is imperative to predict device performance (characteristics) easily and precisely in the manufacture of a semiconductor integrated circuit. To this end, it is necessary to adjust, that is, extract a parameter (to be referred to as a model parameter hereinafter) based on the physical model set by the simulator appropriately. Such adjustment or extraction is made by a model parameter extracting apparatus. Using the apparatus, a model parameter is adjusted to conform to the characteristics of an experimental device in the required manufacturing conditions and to optimize the manufacturing conditions. Therefore, the model parameter extracting apparatus plays an important role.
Meanwhile, the above-described simulation supposes a certain physical model and obtains various characteristic values by calculation based on the model. The characteristic values (to be referred to as target characteristic values hereinafter) obtained by the simulation are associated with a relevant certain physical value and a model parameter associating them is obtained. Finally, the model parameter is adjusted so that the target characteristic values and characteristic values obtained by the actual measurement (to be referred to as actual characteristic values hereinafter) fall within a certain allowable range.
For the adjustment of the model parameter, the relationship between the target characteristic values and the physical quantity is first obtained. The model parameter is determined to satisfy the relationship. In many cases, target characteristic values are discrete with respect to a physical quantity and it is often impossible to obtain the relationship between the target characteristic values and the actual characteristic values. To obtain the relationship, therefore, RSM (Response Surface Methodology) of the design of experiment disclosed by, for example, a reference titled "IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 7, NO. 1, FEBRUARY 1994" has been conventionally used. By using the RSM, an RSF (Response Surface Function) is obtained and target characteristic values continuously corresponding to the change in a physical quantity by using the RSF. As a result, the comparison between the target characteristic value and the actual characteristic value is made possible, thereby adjusting the model parameter such that the target characteristic value and the actual characteristic value fall within a certain allowable range.
However, the above-described conventional parameter adjustment (or extraction) has disadvantages (1) to (3) as follows:
(1) It is rare that an optimum parameter to conform to the target characteristic value falls within a model parameter first set. This makes it difficult to set the adjustment range of the model parameter and requires manual work to update the parameter, that is, to reset the adjustment range of the model parameter. PA1 (2) If the number of model parameters increases, the number of simulation for making an RSF increases. As a result, calculating time is lengthened. PA1 (3) There are cases where such a model parameter capable of making target characteristic values and actual characteristic values fall within an allowable range cannot be obtained only by making a physical model used in the process, device or circuit simulation.
An object of the present invention is to provide a model parameter extracting method and a model parameter extracting apparatus capable of realizing the full automation of the apparatus by automatically re-setting the adjustment range of a model parameter, capable of reducing the number of simulation operations, that is, shortening calculating time by narrowing down the number of parameters and capable of keeping target characteristic values and actual characteristic values within an allowable range.